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Select the graph which satisfies all of the given conditions. f' (-3) = f' (2) = 0 Increasing on (-3, 2) U (2, 00) Decreasing on (-0, –3) g" (-) = f" (2) = 0 Concave upward on (-00,-)U(2, 00) Concave downward on (-,2)

Select the graph which satisfies all of the given conditions. f' (-3) = f' (2) = 0 Increasing on (-3, 2) U (2, 00) Decreasing on (-0, –3) g" (-) = f" (2) = 0 Concave upward on (-00,-)U(2, 00) Concave downward on (-,2)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Select the graph which satisfies all of the given conditions.

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**Select the graph which satisfies all of the given conditions.** - \( f'(-3) = f'(2) = 0 \) - Increasing on \((-3, 2) \cup (2, \infty)\) - Decreasing on \((-\infty, -3)\) - \( f''\left(-\frac{4}{3}\right) = f''(2) = 0 \) - Concave upward on \((-\infty, -\frac{4}{3}) \cup (2, \infty)\) - Concave downward on \(\left(-\frac{4}{3}, 2\right)\)
Transcribed Image Text:**Select the graph which satisfies all of the given conditions.** - \( f'(-3) = f'(2) = 0 \) - Increasing on \((-3, 2) \cup (2, \infty)\) - Decreasing on \((-\infty, -3)\) - \( f''\left(-\frac{4}{3}\right) = f''(2) = 0 \) - Concave upward on \((-\infty, -\frac{4}{3}) \cup (2, \infty)\) - Concave downward on \(\left(-\frac{4}{3}, 2\right)\)
The image contains five graphs displaying different polynomial functions. Each graph has the following characteristics: 1. **Graph 1:** - The curve starts below the x-axis, moves above it, and then sharply descends. - It then rises again, displaying a local maximum. - Finally, the graph curves upwards steeply, crossing the x-axis. - The y-axis is labeled from -60 to 60, and the x-axis centers at 0. 2. **Graph 2:** - The curve shows a similar initial dip and peak as Graph 1, but then it has a higher rising curve. - This time, there is another dip, before rising into a steep incline. - The axes are similarly scaled to the first graph. 3. **Graph 3:** - The curve begins with a downward slope, crosses the x-axis, and peaks before descending sharply. - After reaching a local minimum, it climbs again and crosses the x-axis. - This graph has a focus on a balance between positive and negative y-axis values. 4. **Graph 4:** - It has a steep initial decline to a local minimum, followed by a small peak and then another decline. - There is another rise afterwards. - The graph fluctuates above and below the x-axis, covering both positive and negative values. 5. **Graph 5:** - The pattern starts with a steep initial rise, reaching a local maximum. - It follows with a steep descent dipping below the x-axis, and then another rise. - The function displays a tight set of fluctuating values, crossing the x-axis multiple times. Overall, each graph represents a distinct polynomial function, characterized by varying degrees and behavior of curves. They highlight concepts such as local maxima and minima, inflection points, and x-axis intersections which are critical in understanding polynomial behavior.
Transcribed Image Text:The image contains five graphs displaying different polynomial functions. Each graph has the following characteristics: 1. **Graph 1:** - The curve starts below the x-axis, moves above it, and then sharply descends. - It then rises again, displaying a local maximum. - Finally, the graph curves upwards steeply, crossing the x-axis. - The y-axis is labeled from -60 to 60, and the x-axis centers at 0. 2. **Graph 2:** - The curve shows a similar initial dip and peak as Graph 1, but then it has a higher rising curve. - This time, there is another dip, before rising into a steep incline. - The axes are similarly scaled to the first graph. 3. **Graph 3:** - The curve begins with a downward slope, crosses the x-axis, and peaks before descending sharply. - After reaching a local minimum, it climbs again and crosses the x-axis. - This graph has a focus on a balance between positive and negative y-axis values. 4. **Graph 4:** - It has a steep initial decline to a local minimum, followed by a small peak and then another decline. - There is another rise afterwards. - The graph fluctuates above and below the x-axis, covering both positive and negative values. 5. **Graph 5:** - The pattern starts with a steep initial rise, reaching a local maximum. - It follows with a steep descent dipping below the x-axis, and then another rise. - The function displays a tight set of fluctuating values, crossing the x-axis multiple times. Overall, each graph represents a distinct polynomial function, characterized by varying degrees and behavior of curves. They highlight concepts such as local maxima and minima, inflection points, and x-axis intersections which are critical in understanding polynomial behavior.
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